US President Donald Trump would welcome the chance to run against Oprah Winfrey in 2020 if she chooses to become a presidential candidate, the White House has said.

"We welcome the challenge, whether it be Oprah Winfrey or anybody else," White House spokesman Hogan Gidley told reporters on Monday while travelling aboard Air Force One with the President to Tennessee. 

Gidley said Trump is "absolutely … going to run for President again" and said his record would stack up against any opponent, the Hill magazine reported. 

"Regardless of who decides to run against this President, they are going to have to face a President who has record-setting achievements in a record-setting time," he said. 

Gidley said he did not know whether Trump had seen Winfrey's address on Sunday at the Golden Globes awards, which touched on sexual harassment and racial justice. Her remarks sparked talk on social media and in Hollywood that she could take on Trump in 2020 if he runs again. 

CNN reported that the former television host was "actively considering" a run, citing unnamed sources. Winfrey's longtime partner Steadman Graham told the Los Angeles Times "she would absolutely do it", but added that "it's up to the people".

However, a source told NBC News that Oprah had no intention of running for the President. "It's not happening. She has no intention of running," the source said.

Trump himself has praised Winfrey on several occasions, even once floating her as a possible vice presidential pick before his own official entry into politics.

Winfrey is a longtime supporter of Democrats. She supported Barack Obama's presidential campaign in 2008 and endorsed Hillary Clinton in her 2016 run against Trump.